Exercice

Calculer les intégrales suivantes
a) \(I = \) \(\int {\frac{{\sqrt x }}{{\sqrt[4]{{{x^3}}} + 1}}} dx\)
b) \(I = \) \(\int {\frac{{\sqrt {{x^3}} - \sqrt[3]{x}}}{{6\sqrt[4]{x}}}} dx\)

c) \(I = \) \(\int {\frac{{\sqrt[6]{x} + 1}}{{\sqrt[6]{{{x^7}}} + \sqrt[4]{{{x^5}}}}}} \) \(dx\)
d) \(I = \) \(\int {\frac{{\sqrt[3]{x} + 2}}{{\sqrt[6]{x} + \sqrt[3]{x} + \sqrt x + 1}}} \) \(dx\)

e) \(I = \) \(\int {\sqrt {\frac{{1 - x}}{{1 + x}}} \frac{{dx}}{{{x^2}}}} \)
f) \(I = \) \(\int {\sqrt {\frac{{2 + 3x}}{{x - 1}}} } dx\)